Bifurcation of Periodic Solutions in the General Case

Abstract

In this chapter we shall show that the analysis of bifurcation of periodic solutions from steady ones in R2, which was discussed in Chapter VII, also applies in Rn and in infinite dimensions; say, for partial differential equations and for functional differential equations, when the steady solution loses stability at a simple, complex-valued eigenvalue. The mathematical analysis is framed in terms of the autonomous evolution equation (VI.45) reduced to local form and the analysis of the loss of stability of the solution u = 0 given in §VII.9 is valid for the present problem.